Braess's Paradox - Equilibria Gone Wild

this episode is made possible by Robo race the first electric racing series to combine human and machine intelligence hi everyone Jade here would you like to hear a story in 1968 the city of Seoul in South Korea built a six-lane highway above the chun-yin River in an effort to improve traffic flow it worked at first but as the years passed more and more cars began to appear until finally if one looked over at the highway from their balcony all they would see what caused jammed back to back and the honking of disgruntled drivers in 2005 the mayor of Seoul initiated a project to tear down the highway and revitalize the river this was met with much controversy as if this major road was already jammed up with cars removing it would surely make traffic worse all around the city but to everyone's surprise when the road was torn down travel flow improved in the city of Seoul with travel times for its citizens actually decreasing hello this video is about a phenomenon called braces paradox discovered by a German mathematician dear trick of brace as he was working on modeling traffic he noticed that contrary to intuition adding an extra Road to a traffic network could actually make travel times longer he is how imagine there are two cities origin and destination two roads connect these cities upper road and a lower road there is a point halfway through each road called halfway point where the road changes slightly from the start of upper road to the halfway point of upper road the road is quite narrow and travel time depends on the number of cars on the road the exact time works out to be the number of cars divided by 100 for example if there are 1000 cars on the road it'll take each car 10 minutes to get from the city of origin to the halfway point there the road changes and becomes a six-lane highway now it doesn't matter how many cars are on this highway it always takes the same amount of time 45 minutes lower Road has the same setup except reversed now let's say there are 4,000 drivers who want to get from origin to destination if they all take up a road it'll take each driver 4000 divided by 100 minutes which is 40 minutes plus the fixed 45 minutes of the highway making the total commute time 85 minutes this is obviously a silly strategy a rational driver has incentive to switch to lower road because that would only take them 45 minutes plus one divided by 100 minutes which is roughly 45 minutes a saving of 40 whole minutes other drivers on upper road would also want to change to lower road this pattern would continue until half the drivers take upper road and half take lower road with both roads taking the exact same time of 65 minutes this is a natural equilibrium a driver on upper road has no incentive to switch to lower road as it will only take them longer and a driver on lower road has no incentive to switch to upper road for the same reason this situation where no one has any incentive to change their behavior is called the Nash equilibrium in game theory the key word here is equilibrium which can be thought of as another way of saying when the system is stable opposing forces are equally balanced and the system will not change unless acted upon for example this balancing stick is in equilibrium it won't falter unless there's an outside force like wind or a monkey with half the drivers split evenly between roads no one has any incentive to move so the system will continue going on this way each driver with a total travel time of 65 minutes now let's spice things up let's add a new highway connecting the halfway points of the two roads will call it brace road it's a very wide highway and it takes virtually no time at all to get from one end to the other so for simplicity we're going to say it takes zero minutes Blanche a regular upper road commuter longs for more adventure in life and decides to try out this new highway to her surprise it only takes her 2000 / 100 minutes Plus 2001 / 100 minutes which is roughly 40 minutes to arrive at destination this is a saving of 25 minutes from her usual route more upper road regulars catch on to Blanche's shenanigans and start to use this new route too soon the number of drivers trying this new route reaches 2500 so their travel time is 65 minutes which is now the same total time as the original other Road route they all started on meanwhile the regular lower road drivers are slowed to 85 minutes which is a 20 minute increase before these pesky upper road drivers decided to invade their turf so now they have incentive to change to the new route - with everyone taking this new route it takes each driver 4,000 / 100 minutes plus another 4,000 / 100 minutes 18 minutes to drive from origin to destination a 15 minute increase from their old route so why don't they change back well no one has any incentive - if people made an agreement to go back to their original routes there would always be that annoying driver who selfishly uses the new brace highway to cut down their own travel time soon other drivers will see what he's doing and feel ripped off so they'll do it - before we know it we'll be right back to where we started systems tend to move toward their natural equilibrium just try and stop hot and cold water from mixing into warm water with the introduction of the new road the system's equilibrium has changed and become less efficient this is braces paradox and when we analyze it we see that it isn't really a paradox at all but follows from one very simple fact people are selfish what's best for the individual often isn't what's best for everyone this same behavior has been seen in other parts of life - one study showed that removing the star player from a basketball team can actually improve the team's performance adding extra products to the marketplace can often lead to worse choices made by the consumers the effect has even been seen in medicine where the removal of certain enzymes can lead to an overall improvement in the metabolism the message of this video isn't people as selfish and stop being so selfish the message is actually it's not your fault see this counterintuitive behavior isn't just caused by people's decisions it's to do with something much deeper about the nature of natural equilibrium just so we don't have to feel bad about our selfish human nature I'm going to show you how braces paradox affects even a physical nonliving system like this setup we have here where I'm pretty sure nothing is a conscious decision maker capable of being selfish here we have a water bottle filled with water which is acting as a weight it's hanging from a bar connected to two springs and two strings now the way that the springs and strings are connected is a bit hard to see and it's very important so listen carefully tied to the bar is a regular piece of string which doesn't stretch or anything fancy like that it's then tied to the lower spring which is connected to the wait another spring is also tied to the bar and then tied to the lower string which is connected to the wait to however and this part is very important the two springs are linked together you'll see that both the strings are actually slack at the moment there's no tension pulling on them this is because they're both longer than the springs right now and as the springs are linked together the strings are kind of just hanging there at the moment our spring strings set up has a total length of about 795 millimeters from the bar to the pencil now if I unlink the springs what do you think will happen will the wait a full B rise or C stay the same pause the video now and try to figure it out for yourself go back and listen to the explanation again if you have to alright let's take a look [Music] congratulations to those of you who chose be the weight rose if you didn't get it don't worry you're not alone my intuition tells me that the weight will fall the strings were slack so if we unlink the springs the string should stretch to full length making this setup longer and so lowering the weight but that's not what happened see when the springs were linked they alone were bearing the entire weight of the water bottle there was more tension pulling on them making them stretch more when they're unlinked the wave divides equally between each pair of string and spring link so now each one only bears half the weight of the bottle so even though there was a lengthening in the system here the reduced weight on the springs cause them to compress and therefore become shorter making the total effect an overall shortening of the system and the weight rising if you're into circuits you can think of the before setup as being in series and the after setup as being in parallel for clarity let's compare this setup to the traffic scenario so we can see that it is in fact braces paradox at play the length of the strings and Springs or the height of the weight can be thought of as the travel time of the cause it's the cost or the thing that we're trying to reduce the weight is analogous to the number of cars on the road it can be thought of as the load that we're trying to handle most efficiently the strings are analogous to the 45 minute highways as their length that doesn't change depending on the conditions just as the travel time on the highway didn't change depending on how many cars were on it the springs are analogous to the narrow roads as the length of them does depend on the load just as the narrow roads travel time depends on the amount of cars on them and finally the linking of the springs is analogous to the new brace highway just as the removal of the brace highway from the road network changed the equilibrium of the traffic network to a more efficient one so to the unlinking of the springs changed the equilibrium of the set up to a more efficient one this same behavior has been seen in other physical systems too like electrical circuits water pipes the internet anything to do with heat flow basically anything that can be thought of as a network can fall victim to brace this paradox so even though in some cases your selfishness makes conditions worse for everyone it's not your fault it's a fundamental phenomenon of nature and you can't be blamed for that but seriously I think it's pretty cool that equilibrium points can have such strange behavior we usually think of them as pretty boring lukewarm areas where nothing that interesting happens scientists tend to be more fascinated with behavior that happens at extremes far away from equilibrium points like hurricanes and earthquakes and galaxy formation and the creation of life so I think it's pretty fascinating that even areas we think of mundane and normal can exhibit such counterintuitive behavior it really goes to show that there's no part of science that isn't interesting fascinating as it may be in most cases bracers paradox is an annoying problem that we want to get rid of it could be costing billions of dollars per year in inefficient road networks and slow internet and low-pressure water pipes so can we do anything about it well like most things in life if you want to fix something you first need to identify it the first question we should be asking is is there a way to identify when braces paradox is slowing down a network well the thing about networks is that it's hard to change a part of a network without affecting the whole thing what's more is that it's hard to see how changing part of a network will affect the whole thing if we remove this piece of road it could improve traffic in its local region but how do we know it's not making traffic worse over here there's a common engineering folklore that a local improvement may only transfer the problem somewhere else the way the system is connected and how different parts affect each other isn't obvious and the only way we've figured out how to analyze it so far is by running computer simulations removing a road here plugging it into a computer and seeing how it affects the overall traffic then maybe removing a road here and running the simulation again to see if it's more efficient rinse and repeat the number of possible variations is given by 2 ^ the number of roads so in a small traffic network of about 10 roads this would be fine they'd be just over 1,000 variations so we could just plug them all into a computer simulation and see which one is the most efficient a pretty ordinary computer could manage this calculation pretty quickly however if we take a city with 100 roads things get complicated fast - to the 100th power is this gigantic number it would take the fastest computer in existence today 3 billion years to run all the possible simulations and see which one works best in reality there are a lot more than 100 roads in any major city so the only method we've figured out so far to detect bracers paradox isn't practical with today's computing power this sounds like pretty bad news but not all hope is lost most approaches to solving the paradox so far have focused on figuring out the best network structure but what if instead we focused on changing the way that the cars interact one interesting Avenue researchers are exploring to reduce braces paradox is the idea of collective intelligence basically meaning that instead of each person acting as an individual everyone acts together as a whole to try and reach the optimal state this solution may be close to becoming a reality with the recent progress in self-driving cars self-driving cars would act more like a hive mind with each car being electronically connected to all the others they could be controlled by some kind of central intelligence whose aim is to optimize traffic flow for the system as a whole getting rid of the whole game theoretic aspect of the problem what causes the paradox in the first place is people acting selfishly or at least acting as individuals with the cars acting as a single mind there are no longer individual in to consider so in theory this should sidestep the paradox altogether we're actually beginning to see the first application of swarm intelligence in autonomous car racing at the beginning of May Robo race the world's first AI driverless electric racing series competition saw two of its autonomous cars complete the world's first self-driving car race in Monte Blanco their self-driving cars which they call Robo cars are able to communicate with each other through the use of various sensors installed to maintain awareness of their surroundings car to car communication could be used to find the most efficient route for all cars on a road making braces paradox and traffic networks a problem of the past racing has a history of using competition to encourage technological development before rolling these developments out for mass production Robo race aims to accelerate the development of autonomous vehicle technology through the use of competitions and challenges which are part of the Robo race entertainment platform the game is simple the team with the best a AI wins if you'd like to learn more about what Robo race is doing you can see the videos in there show me how it works playlist join their mailing list for updates on upcoming races or follow them on Instagram to check out their latest models links to all of these are in the description I think braces paradox can teach us a lot of important life lessons sometimes less really is more acting selfishly usually makes things worse for everyone including yourself your natural state often isn't your most efficient state and sometimes the solution you think is best can have catastrophic ly terrible consequences but I want to know what you think what important life lessons can we learn from braces paradox let me know your thoughts in the comments below [Music]

Channel: Up and Atom

Views: 320,372

Rating: 4.9249964 out of 5

Keywords: roborace, braess's paradox, braess, braess's, braess's paradox of traffic flow, braess paradox example, braess paradox spring, braess paradox game theory, paradox, nash equilibrium, network theory, braess paradox, game theory, economics, power grid, price of anarchy, dominant strategy, mathematics, up and atom, paradoja de braess, ewing paradox, physics, math, networks, computer science, equilibrium, nash, machine learning, grand central terminal, social dilemma, microeconomics

Id: cALezV_Fwi0

Length: 17min 3sec (1023 seconds)

Published: Sun Jun 02 2019

Reddit Comments

[u/BezoCCCP]

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[u/ChumbaWumbaParty]

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